Question

Mrs. Lee randomly surveyed 25 of her 125 students about their pets. Her survey

pidicated that 14 students have a dog, 7 students have a cat, 2 students have
another kind of pet, and 8 students have no pet. (Note that some students have
more than one pet). What is Mrs. Lee's best estimate of the total number of her
tudents who have a dog?

Answer 1

My figure would have 3 overlapping regions, each representing dogs, cats, or fish. The overlapping parts represent those areas where owners have more than one pet.

Now, we know the number owners that have dogs is 14 (place this number outside one of the 3 large regions and call it dogs. Do the same for cats (10) and fish (5). At this point it's important to remember that only some of the 14 dog owners have only dogs. Same for cats and fish.

In fact, we know that 4 owners have both dogs and cats. So, on the figure where the dog region and cat region overlap, write 4. Do the same where the dog and fish regions overlap and write 3.

What this means is that of the 14 dog owners, 7 of them own more than a dog. So, 7 dog owners own only dogs:

14 - 7 = 7

Use the same approach for each of the other pets:

Cats: 10 owners have cats; 4 have dogs and cats and 1 has a cat and a fish. So, 5 owners have only cats (10 - 5).

Fish: 5 owners have fish; 3 have dogs and fish and 1 has a cat and a fish. So 1 owner has only fish (5 - 4).

Then, in summary:

Owners that have:

Only Dogs - 7

Only Cats - 5

Only Fish - 1

Dogs AND Cats - 4

Dogs AND Fish - 3

Cats AND Fish - 1

The total number of owners that have at least one pet then is:

7 + 5 + 1 + 4 + 3 + 1 = 21

So, since there are 26 total owners, 5 must not own a dog, cat, or fish.

hope it helps!!!!!!!!!!!!!!!!!!!

I put lot's of work into it